capacity evaluation of eight bolt extended …

Advanced Steel Construction – Vol. 17 No. 3 (2021) 273–282 DOI:10.18057/IJASC.2021.17.3.6

273

CAPACITY EVALUATION OF EIGHT BOLT EXTENDED ENDPLATE MOMENT

CONNECTIONS SUBJECTED TO COLUMN REMOVAL SCENARIO

Ehsan Ahmadi 1, 2 and Seied Ahmad Hosseini 3, *

1 Department of Civil Engineering, Islamic Azad University, Tehran, Iran

2 Beton Wall Co., Tehran, Iran

3 Faculty of Passive Defense, Malek Ashtar University of Technology, Iran

* (Corresponding author: E-mail: [email protected])

A B S T R A C T A R T I C L E H I S T O R Y

The extended stiffened endplate (8ES) connection is broadly used in the seismic load-resisting parts of steel structures.

This connection is prequalified based on the AISC 358 standard, especially for seismic regions. To study this connection’s

behaviors, in the event of accidental loss of a column, the finite element model results were verified against the available

experimental data. A parametric study using the finite element method was then carried out to investigate these numerical

models’ maximum capacity and effective parameters' effect on their maximum capacity in a column loss scenario. This

parametric analysis demonstrated that these connections fail at the large displacement due to the catenary action mode at

the rib stiffener's vicinity. The carrying capacity, PEEQ, Von-Mises stress, middle column force-displacement, critical

bolt axial load, and the beam axial load curves were discussed. Finally, using the Least Square Method (LSM), a formula

is presented to determine the displacement at the maximum capacity of these connections. This formula can be used in

this study's presented method to determine the maximum load capacity of the 8ES connections in a column loss scenario.

Received:

Revised:

Accepted:

9 July 2020

25 March 2021

30 March 2021

K E Y W O R D S

Bolted endplate connection;

Finite element analysis;

Catenary action;

Column loss scenario;

Theoretical model

Copyright © 2021 by The Hong Kong Institute of Steel Construction. All rights reserved.

1. Introduction

The need for structural resistance against progressive failure became

obvious after the progressive collapse of famous towers globally, and structural

safety has become one of the most significant worries in the design of structures.

Based on the definition of progressive collapse in the GSA design code [1],

progressive collapse is the local damage of a structural element that causes

connected components' failure. Therefore, the overall failure of the structure is

much greater than the initial damage. In the last few decades, researchers

realized that by providing sufficient continuity, ductility, and indeterminacy in

the structures, they could prevent this phenomenon. Besides, different

standards development committees were attracting to revising the standards'

design procedure that only local failure was happening in the structure. The

GSA [1] and the US Department of Defense (DOD), and the UFC [2]

conducted comprehensive research in this field.

One of the effective solutions mentioned in these guidelines to decreasing

the damage caused by progressive collapse is the alternate load path method

(APM). In this method, after abnormal load damage a middle column, the

structure seeks an alternative load path to survive from major collapse by

redistributing this load on damaged members with a catenary action mechanism.

Fig. 1 shows the formation of catenary behavior in the beams due to the

column's sudden removal. At the first stage, the beams resist the vertical loads

through their flexural stiffness, and then as the displacements increase

downwards, the beams act as cables between the columns, creating significant

tensile forces that the beam-column joints must be able to resist [3]. It should be

noted that the demand created in a column removal scenario is different from

the earthquake situation. In fact, in these two situations, the internal forces

generated to affect the structure's behavior. Therefore, evaluating beam to

column joints in a column removal scenario is essential to preventing

progressive collapse [4]. Although extensive research studies have been done

according to the behavior of connections under different loading type and

boundary conditions, up to now, many of these research are related to welded

joints or connections under seismic loads, and very few ones are about beam to

column bolted steel joints under column removal scenario. In the following

paragraphs, some of these research are reviewed.

AstanehAsl et al. [5] have conducted four full-scale tests to investigate the

cable-supported floor's catenary action in a column removal scenario. The test

indicates that using the cable on the floor could extend the middle column's

catenary action and displacement. Khandelwal and El-Tawil [6] carried out the

numerical investigation on the welded connections to evaluate the parameters

which affect the formation of catenary action. Their study shows that in the

special steel moment frame, which is designed seismically, parameters like the

beam depth or detail of the beam's web to column play a significant role in a

column removal scenario. Also, Sadek et al. [7] conducted a comprehensive

study of steel moment connections subjected to column removal scenario to

investigate welded connections similar to Khandelwal and El-Tawil [6]. In

2008, Demonceau [8] carried out an experimental test to investigate two main

objects: the progress of catenary action and the study of the behavior of

connections subjected to conventional loading. The performance of welded

moment connection and side-plate moment connections subjected to blast load

was investigated by Karns et al. [9] in experimental test and numerical

modeling analysis. Yang and Tan [10-13] investigated experimental and

numerical simulations to evaluate the behavior of various simple and semi-rigid

connections. They indicated that as the current acceptance criteria consider

connections test for flexural only, the rotation capacity for these connections is

too conservative, and component-based models are essential to designing

structures in a column removal scenario. In 2018, Meng et al. [14] conducted an

experimental and numerical analysis on welded unreinforced flange-bolted web

connections to investigate these connections' performance with two beams and

three columns with different span ratios against column removal scenario.

According to the progressive collapse and column removal scenario, further

studies can be found in [15-20].

Also, some experimental tests were done by Yan et al. at the University of

Sydney to investigate the behavior of steel connections such as bolted endplate

and double web angle connections. The tests were conducted until the failure of

connections to investigate their behavior's full range [21]. Faridmehr et al. [22]

done some experimental tests for examining the classification index of endplate

connections. They suggested a new classification index for these connections

based on the rigidity, ductility requirement, and capacity level. More

experimental and numerical investigation was done by Jayachandran et al. [23]

to evaluate the behavior of bolted endplate connections. Their study had eight

endplate connections with extended endplate in tension side, which then

simulated using ABAQUS software and validated by experimental data to

reconsider the Frye-Morris polynomial model.

M

M M

M

T T TT

Flexural phase

Catenary phase

Fig. 1 Schematic formation of catenary action in beams [3]

Ehsan Ahmadi and Seied Ahmad Hosseini 274

Regarding the presented previous paragraphs, an insignificant number of

researchers investigated the behavior of bolted steel moment connections

against the column removal scenario, and most research has been done on

welded joints. Moreover, the literature review recommends that one of the key

mechanisms is considering catenary action in the column removal analysis,

which leads to extending a system's capacity in progressive collapse. Therefore,

the finite element models of an endplate connection with two beams and three

columns were established using ABAQUS software to verify the numerical

model. Material constitutive models, element types, material and geometric

nonlinearity, and contact models for bolts and endplates were well proposed.

Based on the numerical verification, nine 8ES connections subjected to

catenary action under a middle column-removal scenario were created using

ABAQUS software. These connections are made by welding the beam to an

endplate section with the endplate's attachment to a column flange using fully

tensioned bolts. Finally, the behavior of these nine numerical models,

Von-Mises stresses, plastic equivalent strain (PEEQ), vertical

load-displacement curves, the fracture modes, and their maximum capacity

under removal of the middle column was evaluated, and at the end, a proposed

formula to calculate the maximum capacity of these connections under column

removal scenario has been conducted.

2. Finite element verification

The FEM assumptions were verified with the experimental test conducted

by Dinu et al. [24]. These experimental tests contain four different connections

designed and fabricated to investigate the behavior of steel frame joints

subjected to the column removal scenario. They were extracted from a

three-bay, four-span plan, and six-story structure with a height of 4000 mm for

each story. The beam length was decreased from 8000 mm to 3000 mm as there

was space limitation in the laboratory [24]. Also, in all experimental tests, the

HEB260 was used for column sections with the reduced flange’s width of 160

mm, and the beam section was IPE220. Fig. 2 illustrates the test setup and the

lateral braces' locations in the test setup, which resist the specimen’s

out-of-plane movements in ref [24].

3000 mm

* Flanges reduced to 160 mm width

Late

ral

rest

rain

ts

Late

ral

rest

rain

ts

Late

ral

rest

rain

ts

IPE 200 IPE 200

3000 mm

HE

B 2

60 *

HE

B 2

60 *

Late

ral

rest

rain

ts

Late

ral

rest

rain

ts

HE

B 2

60 *

10

0 t

on

es

actu

ato

r

Late

ral

rest

rain

ts

Late

ral

rest

rain

ts

In-plane restraint In-plane restraint

Fig. 2 The test setup used in ref [24]

2.1. Generality

The specimen EP of Ref. [24] was model by ABAQUS software [25] to

verify the adopted assumptions for FE modeling. For this specimen, the

geometrical properties are shown in Table 1. It was an interior connection that

a 100 tons actuator on top of the middle column used to test the specimen

under monotonic loading. Fig. 3 presents the geometrical details of specimen

EP in mm dimensions and its photo before loading.

Table 1

Geometrical properties of specimen EP in ref [24]

Specimen EP Beam section IPE 220

Connection type Interior Column section HEB 260*

End-plate Dimensions (mm) 370 × 130 × 16

Bolts No. 10

Diameter (mm) 16

*The width of the flanges reduced to 160 mm.

70 3030

90

90

60

60

75

75

220

HEB 260

35

35

16

IPE 220

Fig. 3 Photos of specimen EP before the test and geometrical details used by [21]

(dimensions are in mm)

Fig. 4 shows the finite element model of specimen EP, which contains four

main parts: columns, beams, endplates, and bolts. The bolts are modeled as a

single part made of three partitioned zones: the shank, the head, and the nut.

The welds are considered rigid and modeled by a tie contact tool, and they are

used to connect the beam to the endplate.

Fig. 4 Finite element model of specimen EP

Due to complex numerical problems in finite element modeling, contacts

between system components usually need special care, so small

surface-to-surface sliding was used in all system component interactions. In

this sliding process, only in the initial stage, the contact defined between the

master and slave nodes [26]. It should be noted that the contacts were defined

between different part of the system like the column flange and endplate, the

bolt nuts and heads with column flange and endplate, and the hole and bolt

shanks of both column flange and end plate by surface to surface formulation to

simulate component’s interaction. In normal behavior, the “hard” contact law

with allowed separation after contact was defined. Besides, tangential behavior

contacts with “Penalty” law with a slip coefficient of 0.3 is assumed.

The general static procedure was used in finite element modeling using the

ABAQUS standard solver. In the “Initial” step, boundary conditions are

defined. In the “Pretension” step, the force in a tightened bolt is modeled using

the bolt load tool. Two methods can apply this load: Applying specification

force or a change in the shank length of bolts. In this study, using the apply

force method and the minimum pre-tensioning load presented in table J3.1 of

AISC 360-16 [27], the tension in a tightened bolt is modeled. Finally,

monotonic loading was applied to the middle column section to simulate the

column loss action.

The C3D8R elements with a reduced integration point are used for the

verification model. Also, to have a regular shape for elements, especially in

critical locations like bolt shanks, holes, and connection locations (200 mm

from left and right of connection), the structured meshing technique is used.

The mesh sensitivity analysis shows that accurate simulation results can be

achieved with the 5 mm mesh size for bolt and hole regions. Also, the mesh size

was increased from 10 mm in connection regions to 50 mm in the regions with

low strain. The other important part of specimens was modeled with three, two,

and two elements in their thickness. Fig. 5 shows the typical finite element

mesh of the test specimen.


Fig. 5 Typical finite element mesh of the specimen EP

2.2. Materials properties and boundary conditions

The material properties were defined from the basis of given test results in

ref [24]. Table 2 presents engineering stress-strain values for specimen EP.

These values converted to the true stress-strain relationship using Eq. 1 to Eq. 3

with combined isotropic/kinematic hardening rule. In these equations, εnorm and

σnorm are the strain and stress obtained from the coupon test, εtrue and σtrue are the

true strain and stress, and 𝜀𝑡𝑟𝑢𝑒𝑝𝑙 is the true plastic mechanical strain.

Table 2

Engineering stress-strain values for different elements of specimen EP used in

ref [24]

Component Fy (Mpa) Fu (Mpa) εfracture (%)

Beam Flange 351 498 22.1

Web 370 497 25.2

Column Flange 393 589 19.5

Web 402 583 20.2

Endplate 305 417 30.9

Bolt 965 1080 10.21

𝜀𝑡𝑟𝑢𝑒 = 𝑙𝑛(1 + 𝜀𝑛𝑜𝑟𝑚) (1)

𝜎𝑡𝑟𝑢𝑒 = 𝜎𝑛𝑜𝑟𝑚(1 + 𝜀𝑛𝑜𝑟𝑚) (2)

𝜀𝑡𝑟𝑢𝑒𝑝𝑙

= 𝜀𝑡𝑟𝑢𝑒 −𝜎𝑡𝑟𝑢𝑒

𝐸 (3)

The boundary conditions are defined similarly to those shown in Fig. 6 to

model the appropriate structural behavior under a column removal event. The

column tip section at both ends of exterior columns and the top of the interior

column are attached to a point and placed into the center of their cross-section.

All DOFs of the exterior column are restrained, and the column loss action is

simulated by applying static vertical displacement at the interior column

reference point until the connection failure.

2.3. Fracture mechanisms

Generally, metals and alloys' failure can be divided into two main

categories; ductile and brittle failure. The ductile fracture usually involves a

large amount of plastic deformation, warning before fracture, and displays in

various ways depending on the material classification, boundary conditions,

and constraint level.

On the other hand, brittle failure has small deformation and occurs

suddenly in a location. The specimen Ep, which is used in the verification

section, may experience various modes of failure (e.g.) the rupture of the weld

line at the bottom of the beam flange, net section rupture at the endplate, bolt

fracture, or beam flange rupture. Despite different types of fracture mechanisms

and methods to simulate the damage in the finite element model, which can be

found in the previous work done by Hedayat et al. [28], the focus of this paper is

on the two types of methods to capture these damages. Firstly, the extended

finite element method (XFEM) [29] use to capture the brittle fracture in the

model (fracture of bolts), and secondly, the PEEQ index captures the highest

fracture potential locations, especially for ductile fracture.

In the first category, a predefine failure mechanism was used to capture the

fracture of bolts. This mechanism consists of two-part: the damage initiation

and damage evolution law. Regarding these two parts of the failure mechanism,

a nominal quadratic strain (QUADE) for damage initiation and energy-based

damage for evolution law was used to verify the specimen [28]. An element's

damage initiation can be captured in the second category by observing the stress

or strain level at different components. Based on the Hedayat et al. [28]

research, the value of PEEQ in the critical parts can be monitored to recognize

the fracture’s initiate of elements and obtained with the results of coupon tests.

The average PEEQ for these components was 0.6 and 0.4 for two steel types of

A36 and A572 plates. In this research, the fracture initiates when any location

reaches the mentioned PEEQ limits. The plastic equivalent strain index is

defined as Eq. 4. This index is used to evaluate nonlinear strain damage and is

defined as follows:

𝑃𝐸𝐸𝑄 =√2

3𝜀𝑖𝑗𝑝𝜀𝑖𝑗𝑝

𝜀𝑦 (4)

Where 𝜀𝑖𝑗𝑝 and εy are the plastic strain and yield strain, respectively. This

method had used to identify the failure of steel components such as shear tab

and bolt in simple conventional connections, and in welded connections, beam

flange, and web, in other researcher's studies [30-36].

Fig. 6 Boundary conditions applied to finite element models

2.4. Verification results

The finite element model was built using strategies mentioned in previous

sections and validated against the experimental results of specimen EP

presented in reference [24] regarding the force and displacement relationship.

As shown in Fig. 7, the initial stiffness, yield strength, accumulated plastic

deformation, and local buckling have good agreement in both experimental and

analytical results.

According to experimental results, the bending deformation of the endplate

near the central column connection was caused yielding to initiate at vertical

displacement and an applied load of 39 mm and 117 kN. After that, flexural

stiffness started to decrease dramatically and reach the purely flexural stage

(the axial force in the beams was nearly zero) with vertical displacement of 154

mm and applies a load of 175 kN. Finally, the specimen experiences a sudden

strength loss by initiating fracture in the bolts in the right beam connection's

external bottom row (near the central column). These failure modes are similar

to the numerical results, as shown in Fig. 8a and Fig. 8b. As shown in this figure,

the proposed fracture mechanism explained in previous sections could provide

a quite accurate prediction for bolts’ fractures.

Overall, the analytical model shows sound accuracy to predict the

experimental results. Also, it is used to investigate the failure mechanism of

extended endplate connections.


Fig. 7 Comparison between the numerical and experimental results of specimen EP

presented in ref [24]

Simulation Test

(a)

Simulation Test

(b)

Fig. 8 Comparison of experimental test and simulation result’s failure modes: a) bending

deformation of the endplate, b) fracture of the bolt in the middle column connection

3. Connection design and modeling

In the previous sections, the numerical simulation was described for

verifying the experimental test done by reference [24]. To investigate the

capacity of different 8ES connections in a column removal scenario, a set of

nine connections were designed with the lateral load-bearing system of the

special moment-resisting frame. For the design of steel elements and the

connections AISC 360-16 [27], AISC 341-16 [37], and AISC 358-16 [38] have

been used. In the connections design, three different beam sections of W21,

W24, and W30 with the column section of W14 were used. The bolts are A490

bolts with diameters of 1, 1 1/8, and 1 1/4 inch, and their threads are excluded

from the shear plane. The beams length calculated with the ratio of Lbeam/dbeam =

12 and column length consider as 13 ft for each specimen. A dead and live load

of 96 psf and 50 psf proposed for calculating gravity loads, respectively. Table

3 shows the geometry and connection parameters of nine specimens. According

to this table, beams depth was varied from 530 to 767 mm, which cause to have

a beam length of 6400 to 9083 mm. It should be mentioned that

width-to-thickness ratios for beam and column elements are limited to AISC

341-16 [37] criteria, which are related to highly ductile members.

According to the guidelines presented in the UFC [2], the frames during a

column removal scenario can be divided to direct influence and indirect

influence regions (see Fig. 9a). In this study, the primary region for capacity

evaluation of connections is the direct influence area. To this end, the simplified

model with an interior column in the center of the model and two adjacent

beams can be considered a double full-span assembly, which can be seen in Fig.

9a. Due to the column's small horizontal deformation and compression, the side

columns’ boundary conditions are simplified to fixed hinge constraints [16,

39-41]. As there is symmetry in the geometry and loading, for all specimens in

this study, the boundary conditions for numerical models were considered as

those shown in Fig. 9b.

Hinge Point

Hinge Point

Hinge Point

Hinge Point

The failure column

Infelection point

Infelection point

Infelection point

Infelection point

Lc Lc

Lb Lb

Indirect influence area Indirect influence areaDirect influence area

(a)

(b)

Fig. 9 a) The double full-span assembly extracted from steel frame b) The typical FE

model of numerical specimens

The displacement-controlled loading was considered in the analysis

procedure, so a vertical displacement was gradually applied to the removed

column until the fracture occurred. It should be noted that this column could

only have vertical displacement. Besides, in FE modeling, beams' lateral

bracing is provided following the AISC 341-16 [37] to resist the affected

beams' out-of-plane movements. In this study, specimens were modeled and

analyzed using ABAQUS software ver. 6.14 [25]. The finite element model

overview with proposed boundary conditions and the connection components

can be seen in Fig. 10.

0

50

100

150

200

0 100 200 300 400

Fo

rce (

kN

)

Displacement (mm)

Experiment

Abaqus


Table 3

Investigated specimens’ details

Model No. Beam Column Endplate Bolt

Section dbeam (mm) bf / tf Zx (mm3) Lbeam (mm) Section dcolumn (mm) Lp (mm) bp (mm) tp (mm) dbolt (mm)

Specimen 1 W21x62 533.4 6.699186992 2359737.216 6400.8 W14x159 381 977.9 254 34.925 25.4

Specimen 2 W21x73 538.48 5.608108108 2818575.008 6461.76 W14x176 386.08 982.98 254 38.1 25.4

Specimen 3 W21x93 548.64 4.52688172 3621541.144 6583.68 W14x233 406.4 993.14 254 34.925 28.575

Specimen 4 W24x76 607.06 6.610294118 3277412.8 7284.72 W14x193 393.7 1051.56 304.8 31.75 25.4

Specimen 5 W24x94 617.22 5.182857143 4162314.256 7406.64 W14x257 416.56 1061.72 304.8 34.925 28.575

Specimen 6 W24x103 622.3 4.591836735 4588377.92 7467.6 W14x283 424.18 1066.8 304.8 34.925 31.75

Specimen 7 W30x108 756.92 6.907894737 5669924.144 9083.04 W14x311 434.34 1201.42 304.8 34.925 31.75

Specimen 8 W30x116 762 6.176470588 6194310.192 9144 W14x342 444.5 1206.5 304.8 38.1 31.75

Specimen 9 W30x124 767.08 5.64516129 6685922.112 9204.96 W14x370 454.66 1211.58 304.8 38.1 31.75

Fig. 10 Typical finite element model of a connection

4. Results and discussion

Nine numerical models for investigating the behavior of 8ES connections

were designed and model using ABAQUS software. In this section, these nine

models' behavior under the column removal scenario and the effects of

effective parameters on connections capacity are discussed. The parameters

which directly or indirectly can affect the connection behavior could be dbeam,

bf-beam/tf-beam, and Zx-beam. The performance of specimen 1 depicts in Fig. 11.

Equivalent plastic strain (PEEQ) contours and Von-Mises stress contours are

shown for the overall finite element modeling at the first fracture time step of

the analysis for this specimen in Fig. 11a and Fig. 11b, respectively. Based on

the research done by [30, 31] and the present study, the high plastic strain and

stress demands in the beam flange near the stiffener rib make the 8ES

connections susceptible to fracture. According to damage mechanisms, which

are supposed in section 2.3, as PEEQ in half of beam flanges width reaches

0.4, fracture initiated and specimen experience the maximum deflection.

Understanding the local failure mechanism is highly dependent on the design

of these connections, hence based on the design of the connections, it can be

seen in Fig. 11a, the plastic hinge in specimens is near the rib stiffener, and

plastic deformations are mainly in this region. Due to the plastic hinge

formation, local buckling occurred in the beam's flange and web near the

stiffener rib. Fig. 17 plotted the deformation, PEEQ, and Von-Mises stress

contour for nine specimens.

The Force-displacement curve illustrates specimen 1 at the onset of the

first fracture in the bottom beam flange in Fig. 11c. Also, the maximum and

fracture point of the specimen has shown in this figure. These points indicate

the maximum ductility and strength capacity of this specimen, which later

derives the proposed formula. Another important curve to monitoring the

critical bolt fracture is Fig. 11d, which illustrates the bolt axial load versus

connection displacement at the first fracture's onset. As can be seen in this

figure, at the first stage, the bolt pretension load was applied (285000 N)

based on the type (A490) and diameter (1 inch) of the bolt. Then, increasing

the middle column’s deflection, the bolt axial force has increased to the

maximum point at the pure flexural stage (no tensile force in beams). After

that, due to the plasticization of beam flange elements, the bolt axial force

becomes constant. Finally, by the initiation of fracture in the beam flange, the

bolt axial load starts to decrease until the full fracture of the beam flange.

Fig. 11 Performance of the specimen 1 a) Equivalent plastic strain distributions (PEEQ) b)

Von-Mises stress c) Force-displacement curve, d) Bolt axial load versus connection

displacement at the onset of the first fracture

Comparison of the vertical displacement–force diagrams are shown in Fig.

12 for nine connections with different properties. Based on the connection’s

properties presented in Table 3, they were divided into three main groups with

different beam depths (W21, W24, and W30). It should be noted that the

significant effect of the plastic section modulus and the value of the beam

flange width to its thickness (bf/tf) has caused a capacity increased in

specimen 3 compared to specimens 4 and 5.

4.1. The effect of parameter dbeam, Zx, bf/tf, and dbolt on the maximum capacity of

specimens

As noted earlier, these connections act so that the major capacity depends

on the beam properties due to beam flange failure in a column removal scenario.

As a result, four parameters of dbeam, Zx, bf/tf, and dbolt that mainly affect these

connections' capacity have been studied. According to Fig. 13, the value of

these four parameters versus each specimen's maximum capacity (PFE-max) is

plotted. For instance, Fig. 13a shows that with increasing parameter dbean, the

system’s overall capacity increases. Also, one of the significant parameters is

the beam plastic section modulus (Zx). As can be seen in Fig. 13b, the

maximum values of the system capacity are directly related to the plastic

section modulus, and even in specimen 3, the system capacity has increased

compared to the specimens with higher beam depth which shows the significant

role of this parameter in the capacity of connections in the column removal

scenario.

Moreover, increasing the size of bolts diameter, the rigidity of connections,

and the overall capacity of connections increased. On the other hand, the ratio

of the beam's parameter flange width to its thickness (bf/tf) has a vice versa

0

200

400

600

800

1000

1200

0 200 400 600 800

Co

nnec

tio

n F

orc

e (K

N)

Connection Displacement (mm)

0

100

200

300

400

500

600

0 200 400 600 800B

olt

Axia

l L

oad

(K

N)Connection Displacement (mm)

(a) (b)

(c) (d)


effect on the maximum capacity of specimens (Fig. 13c). As this ratio increases,

the slenderness of flanges increases, and buckling in the beam flange section

will happen sooner.

Fig. 14 shows the regression method results and the values of multiple R

regarding these connections' capacity. As can be seen in this figure, parameters

like the cross-section of the beam (A), beam depth (dbeam), flange Width (bf),

plastic section modulus (Zx), and bolt diameter (dbolt) have a correlation

coefficient of more than 80%. It shows, in these connections, the properties of

the beam and the diameter of the bolt have a great effect on the connections’

capacity.

Fig. 12 Connection force-displacement curve of the nine numerical model

Fig. 13 The effect of parameter a) dbeam, b) Zx, c) bf/tf, and d) dbolt on the maximum

capacity of specimens

Fig. 14 The values of multiple R regarding the capacity of 8ES endplate connections

Table 4 summarized the connection force and displacement of specimens

at the maximum and fracture points. In this table, the second and third columns

represent the displacement at the maximum force point and the maximum

capacity of different specimens. The two last columns of this table show the

displacement and force at the fracture point for specimens.

Table 4

Summary of the force and displacement of all specimens in the maximum and

fracture points

Model No. ΔFE-max (mm) PFE-max (kN) ΔFE (mm) PFE (kN)

Specimen 1 618.72 1025.32 673.71 1022.03

Specimen 2 573.05 1154.41 697.47 1141.81

Specimen 3 636.44 1497.59 734.83 1484.65

Specimen 4 659.83 1188.48 747.14 1179.48

Specimen 5 611.77 1470.46 784.71 1428.38

Specimen 6 614.37 1600.18 794.88 1543.79

Specimen 7 721.70 1599.93 826.77 1573.49

Specimen 8 726.48 1744.25 843.41 1706.50

Specimen 9 739.11 1879.32 867.26 1829.81

4.2. Effect of catenary action on the capacity of specimens

If the connections have adequate ductility, under large deformations due to

the column removal scenario, significant axial forces are created in the beams,

which is very useful in increasing the system’s resistance. This phenomenon is

called catenary action. The formation and expansion of catenary action in

beams remove the column due to an unusual event. The system is starting to

move down due to heavy loads at the location of the removed column. Initially,

the beams resist the vertical loads through their flexural stiffness, and as the

displacements increase downwards, the upper and lower axis of beams are

yielded, and then the range of tensile stresses in the beam axis will increase at

the cross-section. At very high displacements, the compressive stresses are

eliminated, and the entire cross-section of the beam is in tension. At this point,

the beams act as cables between the columns, creating significant tensile forces

that the joints must be able to resist.

According to the important role of catenary action in increasing the

maximum structure’s capacity in a column removal analysis, the system forces

versus rotation capacity of specimen 1 is created in three states (see Fig. 15); the

0

400

800

1200

1600

2000

0 200 400 600 800 1000 1200

Forc

e (k

N)

Displacement (mm)

Specimen 1

Specimen 2

Specimen 3

Specimen 4

Specimen 5

Specimen 6

Specimen 7

Specimen 8

Specimen 9

Specimen 1

Specimen 2

Specimen 3

Specimen 4

Specimen 5

Specimen 6Specimen 7

Specimen 8

Specimen 9

R² = 0.6798800

1200

1600

2000

500 550 600 650 700 750 800

PF

E-m

ax(k

N)

dbeam (mm)


Specimen 3

Specimen 4

Specimen 5


Specimen 8

Specimen 9

R² = 0.9014800

1200

1600

2000

0 2 4 6 8

PF

E-m

ax(k

N)

Zx (mm3) 百万

(b)

Specimen 1

Specimen 2

Specimen 3

Specimen 4

Specimen 5


Specimen 8

Specimen 9

R² = 0.0806

800

1200

1600

2000

4 4.5 5 5.5 6 6.5 7 7.5 8

PF

E-m

ax (

kN

)

bf / tf

(c)

Specimen 1

Specimen 2

Specimen 3

Specimen 4

Specimen 5

Specimen 6

Specimen 7

Specimen 8

Specimen 9

R² = 0.883

900

1100

1300

1500

1700

1900

2100

0.9 1 1.1 1.2 1.3

PF

E-M

(kN

)

dbolt (in)

(d)

0.99

0.82 0.81 0.79

0.95

0.62

0.44

0.94

0.28

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

A d bf tf Zx bp tp db bf

R

Zx bf / tfdbolttpbptfbfdbeam

(a)


overall force (black line), beam axial force (blue dashed line), and force

resulting from flexural stiffness (red dotted line). It should be noted that the

P-catenary action obtains through the cut inserted in the cross-section of the

beam and Eq.5 and the P-bending calculate by Eq.6 and Eq.7. In these

equations the 𝑀𝑙𝑒𝑓𝑡 and 𝑀𝑟𝑖𝑔ℎ𝑡 are the moments which are obtained from an

inserted cut near the stiffener and the 𝐿ℎ is the distance between plastic hinge

locations based on the AISC 358-16 [38].

Fig. 15 Force–rotation angle curves of the specimen 1

P–Catenaryaction = 2 × T × sin(θ∗)

*θ → The rotation of connection (Fig. 16) (5)

P–bending =(𝑀𝑙𝑒𝑓𝑡 −𝑀𝑟𝑖𝑔ℎ𝑡)

𝐿ℎ× 2 × cos(θ) (6)

Lℎ = L𝐵𝑒𝑎𝑚 − 2 × Sℎ , 𝑆ℎ = 𝑡𝑝 + 𝐿𝑠𝑡𝑖𝑓𝑓𝑛𝑒𝑟 (7)

As shown in Fig. 18, specimens have approximately up to 4% rotational

capacity without the catenary action, while this value is tripled and is about 12%

with its presence. In these diagrams, as the amount of bending force increases,

the catenary action load decreases, and they have a vice versa relationship

with each other. As a result, the contribution of catenary action should be

considered in the acceptance criteria of rotation capacities.

5. Implementing the theoretical model for prediction of the

connection’s capacity

In this section, according to the results obtained from numerical analyzes,

a formula is presented to estimate the maximum capacity of systems with

eight bolt stiffened end plate connections. Fig. 16 shows the free diagram

assumed in the column removal analysis and the force equilibrium in the

middle column. According to this figure, in a column removal scenario, two

important forces in determining the amount of these connections capacity are

the amount of plastic moment on the column face and the catenary action load

in the beam.

MT

V

MT

VP

Fig. 16 The free body diagram showing force and moment in column removal analysis

Based on Fig. 16, the system’s maximum capacity in a column removal

scenario can be written as Eq. 8:

PT = V′ + T′ (8)

V′ is the axial force based on the force equation in the plastic hinge, and

T’ is the corresponding force due to catenary action. The equal force with

plastic hinge moment can be defined as Eq. 9:

V′ = (4 × λ × MP

Lh) × Cos(θ) (9)

Where MP is the plastic moment, λ is a coefficient to consider the plastic

interaction between bending moment (M) and axial force (N) at a plastic beam

region which can be expressed by the Eq. 10, Lh is the distance between

plastic hinge locations, and θ is the beam rotation (rad) at the maximum

capacity point of the specimen and can be written as Eq. 11:

(M

MP

)2 + (N

NP

)2 = 1 (10)

θ = Arc tan∆

Lh (11)

M and N are the moments and axial force, Mp is the plastic bending

capacity, and Np is the critical section's axial capacity and ∆ is the vertical

displacement at the maximum capacity point of the specimen. The

corresponding force with catenary action can be computed by Eq. 12:

T′ = 2 × T × sin(θ) (12)

T is the tensile resistance of connection and obtains from Eq. 13. In this

equation, β is the ratio of the stress in the cross-section to the yield stress and

is considered as 0.33 based on the numerical analysis. Also, A is the beam

cross-section, and Fy is the yield stress.

T = β × Fy × A (13)

Up to this point, only one parameter, the vertical displacement at the

maximum capacity point (Δpredict-max), is unknown. The Least Square Method

was used for predicting this parameter. When the number of equations is more

than the number of unknowns in sets of equations, the LSM is a standard

procedure in regression analysis to estimate this overdetermined systems'

solution. This method is popular among researchers [42], and generally, the

predictive model developed based on the LSM is simple; however, its

accuracy should be investigated to be used as a reliable model. Hence, in this

study, according to values in Table 5, the LSM was utilized to propose an

alternative nonlinear model (see Eq. 14) to predict the vertical displacement at

the maximum capacity point (Δpredict-max).

Table 5

The predicted values of ΔFE-max and the performance of the proposed

LSM-based model

Model No.

dbeam

(mm)

Zx

(mm3)

ΔFE-max

(mm)

Δpredict-max

(mm)

Absolute

Error (%)

Specimen 1 533.40 2359737.22 618.72 613.23 0.9

Specimen 2 538.48 2818575.01 573.05 592.16 3.23

Specimen 3 548.64 3621541.14 636.44 625.87 1.69

Specimen 4 607.06 3277412.80 659.83 640 3.1

Specimen 5 617.22 4162314.26 611.77 611.17 0.1

Specimen 6 622.30 4588377.92 614.37 626.55 1.94

Specimen 7 756.92 5669924.14 721.70 747.68 3.47

Specimen 8 762.00 6194310.19 726.48 728.53 0.28

Specimen 9 767.08 6685922.11 739.11 714.79 3.4

* The average absolute percentage error (AAE): 2.01%

* The maximum absolute percentage error (MAE): 3.47%

0

200

400

600

800

1000

1200

1400

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

P (

kN

)

Rotation (rad)

Specimen 1P-All

P-Catenary action

P-bending

θ θ

T


∆predict−max= 1.745 × A6.253 × d7.124 × bf−1.226 × Zx

−6.199 (14)

The proposed LSM-based model's performance was evaluated using

performance measures AAE and MAE, which are the average absolute

percentage error (AAE) and the maximum absolute percentage error (MAE).

The AAE was calculated using Eq. 15. In this equation, Ti and N are the

predicted output, the actual output obtained from the numerical analysis, and

the number of samples. For the proposed predictive model, AAE and MAE

values are 2.01% and 3.47%, indicating the proposed model's accuracy.

AAE =1

N∑[

|Yi − Ti|

Ti× 100]

N

i=1

(15)

Based on the formula presented for displacement at a maximum capacity

of eight bolt stiffened extended endplate moment connections, the theoretical

values (PT) of PFE-max are obtained and presented in Table 6. The values of

AAE and MAE are 5.34% and 8.15%, indicating the proposed model's high

accuracy level.

Table 6

The predicted values of PFE-max

Model No. Lh (mm) A (mm2) PFE-max (kN) Mp (N.mm) θ (rad) T (N) T' (N) PT (kN) Error (%)

Specimen 1 5561.05 11806.43 1025.32 978288056.32 0.11 1404551.71 309138.85 969.36 5.46%

Specimen 2 5615.66 13870.94 1154.41 1168510733.94 0.11 1650156.38 347368.86 1128.70 2.23%

Specimen 3 5743.93 17612.87 1497.59 1501400419.77 0.11 2095314.84 455713.60 1436.85 4.06%

Specimen 4 6451.32 14451.58 1188.48 1358733411.56 0.10 1719232.69 340553.87 1131.90 4.76%

Specimen 5 6566.89 17870.93 1470.46 1725591432.68 0.09 2126015.43 395160.93 1383.07 5.94%

Specimen 6 6627.85 19548.35 1600.18 1902226776.18 0.09 2325569.22 439032.44 1517.90 5.14%

Specimen 7 8243.29 20451.57 1599.93 2350608802.00 0.09 2433021.26 440751.46 1513.05 5.43%

Specimen 8 8297.90 22064.47 1744.25 2568006147.85 0.09 2624899.91 460325.30 1624.38 6.87%

Specimen 9 8358.86 23548.34 1879.32 2771816159.58 0.09 2801428.27 478532.88 1726.06 8.15%

* The average absolute percentage error (AAE): 5.34%

* The maximum absolute percentage error (MAE): 8.15%

Fig. 17 The deformation, PEEQ, and Von-Mises stress contour for nine specimens


Specimen 1

Specimen 2

Specimen 3

Specimen 4

Specimen 5

Specimen 6

Specimen 7

Specimen 8

Specimen 9

Fig. 18 Summary of Force-rotation angle of nine numerical specimen

6. Conclusion

In this study, the behavior of eight bolt extended endplate moment

connections and their maximum capacity subjected to the column removal

scenario has been investigated. In this regard, a verification of composite of

three columns and two beams under column removal scenario using finite

element modeling against valuable experimental results presented by Dinu et

al. [24] has done, and fracture modes of the analytical model have been

discussed. Based on the verification model, nine 8ES endplate moment

connections were designed by the [27, 37, 38]. The significant results of this

research based on the FE results can be drawn:

1. Based on these nine specimens’ failure mode, the beam properties

significantly affect these connections' maximum capacity.

2. The effect of four parameters of dbeam, Zx, bf/tf, and dbolt has been

investigated on specimens' maximum capacity. It can be observed that based

on the regression method results, parameters like the cross-section of the beam

(A), beam depth (dbeam), flange width (bf), plastic section modulus (Zx), and bolt

diameter (dbolt) have a correlation coefficient of more than 80% unlike the

parameter bf/tf (R=28%) with a maximum capacity of specimens.

3. Regarding the Least Square Method, a formula derived to determine

the displacement at the maximum force capacity of connections. The

performance measures of AAE and MAE for this formula were 2.01% and

3.47%, respectively.

4. According to the proposed theoretical model in section 5, a procedure has

been conducted to determine the maximum capacity of 8ES connections. The

performance measures of AAE and MAE for the proposed method were 5.34%

and 8.15%.

References

[1] Administration, T. U. S. G. S., “Progressive collapse analysis and design guidelines for new

federal office buildings and major modernization projects”, Journal, GSA, Issue, 2003.

[2] (UFC), U. f. c., “Design of building to resist progressive collapse”, 2016.

[3] Daneshvar, H., “One-sided steel shear connections in column removal scenario”, 2013.

[4] Brett, C. and Lu, Y., “Assessment of robustness of structures: Current state of research”,

Frontiers of Structural and Civil Engineering, 7, 4, 356-368, 2013.

[5] Astaneh-Asl, A., et al., “Progressive collapse resistance of steel building floors”, Report

Number UCB/CEE-Steel-2001, 3, 2001.

[6] Khandelwal, K. and El-Tawil, S., “Collapse behavior of steel special moment resisting frame

connections”, Journal of Structural Engineering, 133, 5, 646-655, 2007.

[7] Sadek, F., et al., “An experimental and computational study of steel moment connections

under a column removal scenario”, NIST Technical Note, 1669, 2010.

[8] Demonceau, J.-F., “Steel and composite building frames: sway response under conventional

loading and developmet of membrane effects in beams further to an exceptional action“,

Université de Liège, 2008.

[9] Karns, J. E., et al., “Behavior of varied steel frame connection types subjected to air blast,

debris impact, and/or post-blast progressive collapse load conditions“, Structures Congress

2009: Don't Mess with Structural Engineers: Expanding Our Role. 2009.

[10] Yang, B. and Tan, K., “Behaviour of steel beam-column joints subjected to catenary action

under a column-removal scenario”, Journal of Structural Engineering, ASCE. Submitted for


publication, 2010.

[11] Yang, B. and Tan, K. H., “Numerical analyses of steel beam–column joints subjected to

catenary action”, Journal of Constructional Steel Research, 70, 1-11, 2012.

[12] Yang, B. and Tan, K. H., “Robustness of bolted-angle connections against progressive

collapse: Experimental tests of beam-column joints and development of component-based

models”, Journal of Structural Engineering, 139, 9, 1498-1514, 2013.

[13] Yang, B. and Tan, K. H., “Experimental tests of different types of bolted steel beam–column

joints under a central-column-removal scenario”, Engineering Structures, 54, 112-130, 2013.

[14] Meng, B., Zhong, W., and Hao, J., “Anti-collapse performances of steel beam-to-column

assemblies with different span ratios”, Journal of Constructional Steel Research, 140,

125-138, 2018.

[15] Barmaki, S., Sheidaii, M. R., and Azizpour, O., “Progressive Collapse Resistance of Bolted

Extended End-Plate Moment Connections”, International Journal of Steel Structures, 1-15,

2020.

[16] Lew, H. S., et al., “Performance of steel moment connections under a column removal

scenario. I: Experiments”, Journal of Structural Engineering, 139, 1, 98-107, 2013.

[17] Li, L., et al., “Experimental investigation of beam-to-tubular column moment connections

under column removal scenario”, Journal of Constructional Steel Research, 88, 244-255,

2013.

[18] Li, L., et al., “Effect of beam web bolt arrangement on catenary behaviour of moment

connections”, Journal of Constructional Steel Research, 104, 22-36, 2015.

[19] Qin, X., et al., “Experimental study of through diaphragm connection types under a column

removal scenario”, Journal of Constructional Steel Research, 112, 293-304, 2015.

[20] Qin, X., et al., “A special reinforcing technique to improve resistance of beam-to-tubular

column connections for progressive collapse prevention”, Engineering Structures, 117,

26-39, 2016.

[21] Yan, S., et al., “Experimental evaluation of the full-range behaviour of steel beam-to-column

connections”, Advanced Steel Construction, 16, 1, 77-84, 2020.

[22] Faridmehr, I., et al., “An overview of the connection classification index”, Advanced Steel

Construction, 15, 2, 145-156, 2019.

[23] Arul Jayachandran, S., et al., “Investigations on the behaviour of semi-rigid endplate

connections”, Advanced Steel Construction, 5, 4, 432-451, 2009.

[24] Dinu, F., Marginean, I., and Dubina, D., “Experimental testing and numerical modelling of

steel moment-frame connections under column loss”, Engineering Structures, 151, 861-878,

2017.

[25] “Abaqus 6.14 Analysis User’s Manual”, Journal, Dassault Systems, Issue, 2014.

[26] Krolo, P., Grandić, D., and Bulić, M., “The guidelines for modelling the preloading bolts in

the structural connection using finite element methods”, Journal of Computational

Engineering, 2016, 2016.

[27] ANSI, B., “AISC 360-16, Specification for Structural Steel Buildings”, Chicago AISC,

2016.

[28] Seif, M., et al., “Finite element modeling of structural steel component failure at elevated

temperatures“, Structures. 2016. Elsevier.

[29] Dolbow, J. E., “An extended finite element method with discontinuous enrichment for

applied mechanics”, 2000.

[30] Abou-zidan, A. and Liu, Y., “Numerical study of unstiffened extended shear tab

connections”, Journal of Constructional Steel Research, 107, 70-80, 2015.

[31] Suleiman, M. F., “Non-Linear Finite Element Analysis of Extended Shear Tab Connections“,

Cincinnati, Ohio, USA, 2013.

[32] Morrison, M., Quayyum, S., and Hassan, T., “Performance enhancement of eight bolt

extended endplate moment connections under simulated seismic loading”, Engineering

Structures, 151, 444-458, 2017.

[33] Naimi, S., Celikag, M., and Hedayat, A. A., “Ductility enhancement of post-Northridge

connections by multilongitudinal voids in the beam web”, The Scientific World Journal,

2013, 2013.

[34] Raftari, M., Mahjoub, R., and Hekmati, A., “Evaluation of Damage Indicators of Weld and

Cyclic Response of Steel Moment Frame Connection Using Side Stiffener Plates”, AUT

Journal of Civil Engineering, 1, 1, 67-76, 2017.

[35] Rahnavard, R., Hassanipour, A., and Siahpolo, N., “Analytical study on new types of

reduced beam section moment connections affecting cyclic behavior”, Case Studies in

Structural Engineering, 3, 33-51, 2015.

[36] Ricles, J. M., et al., “Development of improved welded moment connections for

earthquake-resistant design”, Journal of Constructional Steel Research, 58, 5-8, 565-604,

2002.

[37] Seismic, A., “Seismic Provisions for Structural Steel Buildings,(ANSI/AISC 341-16)”,

Journal, American Institute of Steel Construction, Chicago, IL, Issue, 2016.

[38] AISC, A., “AISC 358-16”, Prequalified connections for special and intermediate steel

moment frames for seismic applications. Chicago (IL): American Institute of Steel

Construction, 2016.

[39] Ahmadi, R., et al., “Experimental and numerical evaluation of progressive collapse behavior

in scaled RC beam-column subassemblage”, Shock and Vibration, 2016, 2016.

[40] Sadek, F., et al., “Performance of steel moment connections under a column removal

scenario. II: Analysis”, Journal of Structural Engineering, 139, 1, 108-119, 2013.

[41] Zhong, W., Meng, B., and Hao, J., “Performance of different stiffness connections against

progressive collapse”, Journal of Constructional Steel Research, 135, 162-175, 2017.

[42] Marquardt, D. W., “An algorithm for least-squares estimation of nonlinear parameters”,

Journal of the society for Industrial and Applied Mathematics, 11, 2, 431-441, 1963.

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